Damage Model of Brittle Coal-Rock and Damage Energy Index of Rock Burst

Jun.2003Journal of China University of Mining TechnologyVol 13 NoDamage Model of Brittle Coal-Rock andDamage Energy Index of rock burstYIN Guang-zh(尹光志y2, ZHANG Dong-ming张东明y2WEⅠ Zuo-an(魏作安y2,LIDg-e(李东伟y2(1. Key Lab. for the Exploitation of Southwest Resources and the EnvironmenDisaster Control Engineering, Ministry of Education Chongqing University Chongqing 400044, China2. College of Resource and Environmental Sciences Chongqing University Chongqing 400044, ChinaAbstract: Based on the mechanical experiment of brittle coal-rock and the damage mechanical theory a damage modelas established. Coal-Rock damage mechanical characteristic was researched. Furthermore interior energy transformation mechanism of rock was analyzed from the point of view of damage mechanics and damage energy release rate ofbrittle coal rock was derived. By analyzing the energy transformation of rock burst a new conception damage energyndex of rock burst was put forward. The condition of rock burst was also establishedKey words: coal-rock damage damage energy index rock burstCLC number: TD32 Document code: A Article ID: 1006-1266 2003 X1-0016-0ck from yanshitai coal mine, cho1 IntroductionThen, damage energy index of rock burst and its ocCoal-Rock is a kind of brittle material with o-curring condition are put forwardriginal damage. Its macrofracture failure is a result 2 Damage Constitutive Equation of Brittle Coalof nucleation development and coalescence of interiRockor microcracks. This could be viewed as evolvement, cumulation of damage. Since dougilf 1] apThere are lots of cracks in coal-rock. Under apto rock and concrete materials, Dragorf 2 and other scholars have researched on plied load cracks generate, propagate and interactcontinuous damage of rock and concrete according to with each other to give rise to a degradation of intethe principle and method of damage mechanics andrior characteristics. These phenomena lead to a corablished a correspondingmodel. In China, there are some scholars who have responding macroscopic mechanical responsedone some works to rock damage mechanics. Dong- Macroscopic fracture phenomena of coal-rock are as-cong 3 ]and Xia Mengferf4 5] led damage mechanicssociated with evolvement of microstructures and mito metal materials. Lingjianming 6] and KrajcioviC 7researched on damage mechanics characteristics andcro flawsconstitutive equations of rocklike materials and gotIn 1980, while researching on cracksome useful achievement. Damage constitutive equa- tion and its regularities of distribution about shaletion is established in this paper according to the exund中国煤化 Ty and Kipp3 presentedperimental result of uniaxial compressive test of coal- theHCNMH Ger unit volume in rockReceived date 2002-09-2Foundation item: Doctoral fund of ministry of education, China( 2000061115) the teaching and research award program for outstandingoung teachers in higher education institutions of MOe, P. R C., TRAPOYT)Biography: YIN Guang-zh( 1962-), male from Xichang Prowince, professor Ph. D, doctorial tutor engaged in the reseachon on rock me- and mining engineeringYIN Guang-zhi et alDamage Model of Brittle Coal-Rock and Damage Energyand strain met a relation as followsial compressive test, the constitutirelation parameters Es and n are determined and calhere:N is the cracks per unit volume; eI is culatedstrain k and m are constants of materialig. I and Fig. 2 show typical stress-strain exIt was supposed that damage variable under u- perimental curve under uniaxial load and theoreticalbiaxial compression load isdamage constitutive model curve separately of coal(1) rock specimens 10"and 12 from coal stratum 6"inwhere n is a constant of material: e is axial com- Yanshitai Coal Mine. From Fig. 1 and Fig. 2, theEq (5) could defeati v ccording to conception of effective stress, ef- scribe preferably stress-strain curve of brittle coalck undeaxialBased on equivalence strain principle that pre-sented by Lemaitre, the stain caused by stress ondamaged material is equivalent to strain caused by0255075100125effective stress on undamaged material. That isFig. 1 Brittle coal-rock damage constitutiveD(2)lel and experimental curves( 10 specimencurvewhere: o is stress; E is Youngs modulus'E=EExperimen(1-D) is youngs modulus of damaged material named as effective young s modulusEg.(2)could be expressed byF(1-D025507.5100125Eg. (3)represents the damage constitutive relationof damaged materialFig 2 Brittle coal-rock damage constitutiveWhile substituted D in Eq (3 )with Eq ( 1)model and experimental curves( 12"specimendamage constitutive relation of rock under uniaxial 3 Damage Energy Release Rate of Brittle Coalcompressive load may be expressed byRock and Damage Energy Index of Rock burstg=E(1-me")For damaged material, its elastic strain energyifand elastic residual energy arew(D)=le:E(D):s,(6)thenandThus the damage variable could be showed byoVoD)=Jo:E-(D)Damage energy release rate isAccording to Eg. (3)and Eq cconstitutive equation of rock under uniaxial stress is Y PaDpaD 2ee: dE(D).edye 1dD中国煤化工 and strain equivalenceEvolution equation of damage variable isprCN MH Grial it is known thatσ=(Ⅰ-D)1:a=MD):a,E: M(D)E(D)where Es and n are material parameters of rockFo数据(5) and experimental results of E(D)=E:MD)Journal of China University of Mining TechnologyVol 13 No. 1E(D=M(D):Ematerial has been destroyed while D<1. If damageand M(D=E:E(D)damage energy release rate is ywhere: E(D ) is effective stress tensor M(D ) is e2(1-D2)(9)ual to( I-D)After mathematical manipulation damage enBy Eg (9), failure of coal-rock not only isergy release rate is deducedcaused by state of stress but also depend on evolve-1+yment and accumulation of damage2E(1-D)2F(1-D)In uniaxial compressive experimentsotropic damage energy release rate could bededuced too according to eq (6), that is&e: FweS1=1.(8)If axial strain is e when coal-rock fail, d. andwhere we is elastic strain energy densityY would be expressed asOn the condition of constant load(1-D)Eda=(1-D):de°-E:εdD=0,Yσ:de"=(1-D)":E:de2F(1-D)1 dweed with abrupt and violent destroy of coal-rock massDamage energy release rate Y can be take into around mining field caused by release of elastic enaccount as a function of hydrostatic pressure and ergy in mining 10] A large number of experimentsMisses equivalent stress. If hydrostatic pressureand productive practice prove that coal seam inwhich rock burst occur, suffice to suddenly failureoH3L,o, deviatonic stress tensor will be showed and gain large quantity of elastic deformation eneras:S;=σ-σHgy. That means the prerequisite for the rock burstthat coal seam has outburst tendentiousness. TheTherefore Misses equivalent stressdexes to measure outburst tendentiousness of coalseam are elastic energy index Wet outburst energyndex Wce stiffness ratio index Kce elastic defe2(0-aHI ( o-CHImation index Ki and dynamic failure time DTElastic energy index whic his used to surveyThus Eq (7)is transformed intooutburst tendentiousness, is the ratio of elastic energy to plastic deformation consumed energy. Out2F(1-D)burst energy index is the area ratio of ascendingwhere S,=2(1+v)+31-2v0HStiffness ratio index is the ratio of stiffness value inS, is named as triaxial factor of stress becausefront of peak point of stress-strain curve to value bresponse effect of triaxial ratio of stresshind of it. Elastic deformation index is the ratio ofDamage equivalent stress was defined as followselastic deformation value by repetitive loading to thehat中国煤化工n 80 percent of peaktherefore, y2(1-D)CNMHGme of specimen is theWith load increase damage of coal-rock will e- time between limit load and complete failurevolve continuously till a state of entire fracture. InFig 3 shows a typical stress-strain curve oftheory material is in a state of complete fracture brittle coal-rockwilD万有数握 many experiments indicate thatYIN Guang-zhi et alDamage Model of Brittle Coal-Rock and Damage Energyindex;W。 is elastrain energy ;wd is damage dissipative energ.While We is 1 all the stored elastic strain energywill transform into damage dissipative energyThere is no redundant energy to release. So rockburst is impossible to occur. While wed is greatern coal-rock willFig 3 Stress-Strain curve of brittle coal-rocktransform into damage dissipative energy. The restIn Fig 3, OA is an initial stage of deforma-of elastic strain energy will be release by failure ofion. AB is the elastic stage. In this stage damage coal-rock. Rock burst may occur. The possibility ofeffect is not obvious before peak value B. Most of rock burst occurring increases by Wed. In otherexternal work is reserved in form of elastic strain enwords, rock burst will occur more violent. Thusergy by coal-rock specimen. Internal damage inEq1(11)W>1(11)creases rapidly near and behind peak point this be-haved with softening phase in macroscopic viewis a necessary condition on which rock burst occursSome of stored elastic strain energy can be trans-Based on Eg. 8), the elastic strain energy releasedformed into dissipative energy consumed by damageduring failure of coal-rock after peak point stress unand residual energy will be transformed into kinetic der uniaxial compressive state isenergy while brittle failure of coal-rock specimen. soWs=(1- DB )YB-(1- Dc )YcCD represents the steady residual strength processWd=W。-Ws(12)Therefore the intensity of rock burst is correlatedAccording to stress-strain experimental curvesh release quantitative of elastic straiof coal-rock and Eq (10)to Eq. 12), damage eneral-rock failure and dissipativegy index of rock burst( Wed )can be calculatedby damage evolving. The bigger damage dissipative Furthermore outburst risk will be distinguished. Itenergy is the less release energy is. Thus the possi- is a simple method to calculate Wd than measuringbility of coal-rock burst abruptly and violently will WET, WeF and KcE. This is the merit of WeDbe reduced. Contrariwise, coal-rock will fail sudden-o the method mentioned aboly and release mass elastic strain energy. So, the damage characteristic parameters of two specimensdamage energy index of rock burst could be defined (10*,12*), sampled from 6* coal stratum of Yanshitai Coal Mine, were analyzed. The results arewd Wd(10) listed in Table 1Table 1 The damage characteristic parameters and rock burst damenergy index of 6" coal stratum in yanshitai Coal MineCompressionYoungsDamage characteristic parameters of coal specimenRock burstSpecimenengtnoduldamage energyG /MPaE/MPaYJMPaindex wrd4.260.34×108.75×10-30.0961.15#0.35×10410.00×10-30.421.14H中国煤化工In Table 1, damage energy index of rodCNMHGin 6 coal stratum of Yanshitai Coal Mine is greaterthan 1. Therefore, the coal stratum has risk of rockBased on experimental research of coanalysis a damage constitutive modelpresented. From the point of view of coal-rock damJournal of China University of mining TechnologyVol 13 No. 1age mechanics damage energy release rate of brittle point of energy. Then, the damage characteristiccoal-rock is established. After analyzing the energy parameters and rock burst damage energy index ofstoring dissipating, the rock burst damage energy 6" coal stratum in Yanshitai Coal Mine were calcuindex is presented. 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